In this paper, we answer the question: Given a collection of compact sets, can one decide in polynomial time whether there exists a convex body whose boundary intersects every set in the collection? We prove that already when the sets are segments in the plane, deciding existence of a convex stabber is NP-complete. On the positive side, we give a polynomial-time algorithm (in the full paper) to...

We study a class of geometric stabbing/covering problems for sets of line segments, rays, and lines in the plane. While we demonstrate that the problems on sets of horizontal/vertical line segments are NP-complete, we show that versions involving (parallel) rays or lines are polynomially solvable.

In the Capacitated Arc Stabbing problem (CAS) we are given a set of arcs and a set of points on a circle. We say that a point p covers, or stabs, an arc A if p is contained in A. Each point has a weight and a capacity that determines the number of arcs it may cover. The goal is to find a minimum weight set of points that stabs all the arcs. CAS models a periodic multiitem lot sizing problem in ...

Collaborative research between the disciplines of forensic pathology and biomechanics was undertaken to investigate the hyperelastic properties of human skin, to determine the force required for sharp instrument penetration of skin, and to develop a finite element model, which reflects the mechanisms of sharp instrument penetration. These studies have led to the development of a "stab metric," ...

In a temporal database, each data tuple is accompanied by a time interval during which its attribute values are valid. In this paper, we consider the null time intervals, that is, time intervals not intersected by any time intervals in the temporal database. We deal with the problem of computing temporal aggregates over null time intervals with length constraints. By interval folding, we transf...

A convex polygon that is nearly-similar to a model polygon P has sides parallel and in the same order to the corresponding sides of P. The lengths of the sides are unrestricted and may be zero. Given a set of target convex polygons in the plane with a total of n vertices, and a xed model convex stabbing polygon P, the minimum-perimeter polygon nearly-similar to P that stabs the targets can be f...

Tracheobronchial injuries are closely related to orotracheal intubations and chest traumas. Stabbing injuries are very rare and often life threatening because of the damage to vital structures such as the respiratory tract and large arterial or venous vessels. Early diagnosis and treatment of penetrating neck injuries increase survival rates. We report a case of the tracheobronchial section wit...